The characteristic time constants of the relaxation dynamics of core-excited atoms have hitherto been inferred from the linewidths of electronic transitions measured by continuous-wave extreme ultraviolet or X-ray spectroscopy. Here we demonstrate that a laser-based sampling system, consisting of a few-femtosecond visible light pulse and a synchronized sub-femtosecond soft X-ray pulse, allows us to trace these dynamics directly in the time domain with attosecond resolution. We have measured a lifetime of 7.9(-0.9)(+1.0) fs of M-shell vacancies of krypton in such a pump-probe experiment.

The amplitude and frequency of laser light can be routinely measured and controlled on a femtosecond (10(-15) s) timescale. However, in pulses comprising just a few wave cycles, the amplitude envelope and carrier frequency are not sufficient to characterize and control laser radiation, because evolution of the light field is also influenced by a shift of the carrier wave with respect to the pulse peak. This so-called carrier-envelope phase has been predicted and observed to affect strong-field phenomena, but random shot-to-shot shifts have prevented the reproducible guiding of atomic processes using the electric field of light. Here we report the generation of intense, few-cycle laser pulses with a stable carrier envelope phase that permit the triggering and steering of microscopic motion with an ultimate precision limited only by quantum mechanical uncertainty. Using these reproducible light waveforms, we create light-induced atomic currents in ionized matter; the motion of the electronic wave packets can be controlled on timescales shorter than 250 attoseconds (250 x 10(-18) s). This enables us to control the attosecond temporal structure of coherent soft X-ray emission produced by the atomic currents--these X-ray photons provide a sensitive and intuitive tool for determining the carrier-envelope phase.

In Bohr's model of the hydrogen atom, the electron takes about 150 attoseconds (1 as = 10(-18) s) to orbit around the proton, defining the characteristic timescale for dynamics in the electronic shell of atoms. Recording atomic transients in real time requires excitation and probing on this scale. The recent observation of single sub-femtosecond (1 fs = 10(-15) s) extreme ultraviolet (XUV) light pulses has stimulated the extension of techniques of femtochemistry into the attosecond regime. Here we demonstrate the generation and measurement of single 250-attosecond XUV pulses. We use these pulses to excite atoms, which in turn emit electrons. An intense, waveform-controlled, few cycle laser pulse obtains 'tomographic images' of the time-momentum distribution of the ejected electrons. Tomographic images of primary (photo)electrons yield accurate information of the duration and frequency sweep of the excitation pulse, whereas the same measurements on secondary (Auger) electrons will provide insight into the relaxation dynamics of the electronic shell following excitation. With the current approximately 750-nm laser probe and approximately 100-eV excitation, our transient recorder is capable of resolving atomic electron dynamics within the Bohr orbit time.

The electromagnetic field of visible light performs approximately 10(15) oscillations per second. Although many instruments are sensitive to the amplitude and frequency (or wavelength) of these oscillations, they cannot access the light field itself. We directly observed how the field built up and disappeared in a short, few-cycle pulse of visible laser light by probing the variation of the field strength with a 250-attosecond electron burst. Our apparatus allows complete characterization of few-cycle waves of visible, ultraviolet, and/or infrared light, thereby providing the possibility for controlled and reproducible synthesis of ultrabroadband light waveforms.

Resolving in time the dynamics of light absorption by atoms and molecules, and the electronic rearrangement this induces, is among the most challenging goals of attosecond spectroscopy. The attoclock is an elegant approach to this problem, which encodes ionization times in the strongfield regime. However, the accurate reconstruction of these times from experimental data presents a formidable theoretical challenge. Here, we solve this problem by combining analytical theory with ab-initio numerical simulations. We apply our theory to numerical attoclock experiments on the hydrogen atom to extract ionization time delays and analyse their nature. Strong field ionization is often viewed as optical tunnelling through the barrier created by the field and the core potential. We show that, in the hydrogen atom, optical tunnelling is instantaneous. By calibrating the attoclock using the hydrogen atom, our method opens the way to identify possible delays associated with multielectron dynamics during strong-field ionization.

The multiconfiguration time-dependent Hartree-Fock approach for the description of correlated few-electron dynamics in the presence of strong laser fields is introduced and a comprehensive description of the method is given. Total ionization and electron spectra for the ground and first excited ionic channels are calculated for one-dimensional model systems with up to six active electrons. Strong correlation effects are found in the shape of photoelectron peaks and the dependence of ionization on molecule size.

Photoelectrons excited by extreme ultraviolet or x-ray photons in the presence of a strong laser field generally suffer a spread of their energies due to the absorption and emission of laser photons. We demonstrate that if the emitted electron wave packet is temporally confined to a small fraction of the oscillation period of the interacting light wave, its energy spectrum can be up- or downshifted by many times the laser photon energy without substantial broadening. The light wave can accelerate or decelerate the electron's drift velocity, i.e., steer the electron wave packet like a classical particle. This capability strictly relies on a sub-femtosecond duration of the ionizing x-ray pulse and on its timing to the phase of the light wave with a similar accuracy, offering a simple and potentially single-shot diagnostic tool for attosecond pump-probe spectroscopy.

It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schrödinger equation with strong infrared fields. This is demonstrated by computing high harmonic spectra and wave-function overlaps with the exact solution for a one-dimensional model system and by three-dimensional calculations for the H atom and a Ne atom model. We lay out the key ingredients for correct implementation and identify criteria for efficient discretization.